抄録
This paper deals with a variation of the classical isoperimetric problem in dimension N≥ 2 for a two-phase piecewise constant density whose discontinuity interface is a given hyperplane. We introduce a weighted perimeter functional with three different weights, one for the hyperplane and one for each of the two open half-spaces in which RN gets partitioned. We then consider the problem of characterizing the sets Ω that minimize this weighted perimeter functional under the additional constraint that the volumes of the portions of Ω in the two half-spaces are given. It is shown that the problem admits two kinds of minimizers, which will be called type I and type II, respectively. These minimizers are made of the union of two spherical domes whose angle of incidence satisfies some kind of “Snell’s law”. Finally, we provide a complete classification of the minimizers depending on the various parameters of the problem.
本文言語 | English |
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ページ(範囲) | 7750-7772 |
ページ数 | 23 |
ジャーナル | Journal of Geometric Analysis |
巻 | 31 |
号 | 8 |
DOI | |
出版ステータス | Published - 2021 8月 |
ASJC Scopus subject areas
- 幾何学とトポロジー